On the Computational Complexity of Conservative Computing

  • Giancarlo Mauri
  • Alberto Leporati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


In a seminal paper published in 1982, Fredkin and Toffoli have introduced conservative logic, a mathematical model that allows one to describe computations which reflect some properties of microdynamical laws of Physics, such as reversibility and conservation of the internal energy of the physical system used to perform the computations. In particular, conservativeness is defined as a mathematical property whose goal is to model the conservation of the energy associated to the data which are manipulated during the computation of a logic gate.

Extending such notion to generic gates whose input and output lines may assume a finite number d of truth values, we define conservative computations and we show that they naturally induce a new NP–complete decision problem and an associated NP–hard optimization problem. Moreover, we briefly describe the results of five computer experiments performed to study the behavior of some polynomial time heuristics which give approximate solutions to such optimization problem.

Since the computational primitive underlying conservative logic is the Fredkin gate, we advocate the study of the computational power of Fredkin circuits, that is circuits composed by Fredkin gates. Accordingly, we give some first basic results about the classes of Boolean functions which can be computed through polynomial–size constant–depth Fredkin circuits.


Boolean Function Input Pattern Output Line Disjunctive Normal Form Output Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Giancarlo Mauri
    • 1
  • Alberto Leporati
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano – BicoccaMilanoItaly

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